Algebra and geometry of link homology
arXiv:2108.10356
Abstract
These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, its basic properties and recent advances, as well as three algebro-geometric models for link homology: braid varieties, Hilbert schemes of singular curves and affine Springer fibers, and Hilbert schemes of points on the plane.
49 pages
References in corpus (10)
- Categorification of the braid groups
- Cell decompositions of character varieties
- Augmentations, Fillings, and Clusters
- BFN Springer Theory
- The cohomology ring of certain compactified Jacobians
- Soergel bimodules and matrix factorizations
- Tautological classes and symmetry in Khovanov-Rozansky homology
- From the Hecke Category to the Unipotent Locus
- A categorification of a cyclotomic Hecke algebra
- Affine Springer Fibers, Procesi bundles, and Cherednik algebras